Arrange the net pots -- which are readily available from hydroponics supply stores -- on the bin lid. Leave at least 3 inches between them to allow room for the peppers to grow. Keep them 2 inches from the edges of the lid. Draw around each pot to mark where it should go.
Cut a hole with the keyhole saw at each marked location. Make sure the net pots fit into the holes but cannot fall through. The rims at the top will support them.
Drill a 1/4-inch hole for the air line near the top of one end of the bin. Feed the air line through the hole so that there is enough on the inside of the bin to easily reach the bottom.
Attach the air stone to one end of the air line and connect the other end of the line to the pump. This will add oxygen to the liquid, which is necessary for the roots of the pepper plants.
Add hydroponic nutrient solution to the bin. This solution contains everything the peppers need to support them as they grow. Fill the bin to within an inch of the top. Place the lid on the bin.
Fill each of the net pots with clay pellets, commonly available from hydroponic suppliers. Place a single pepper plant in each pot and carefully cover the roots with the pellets. Set one pot in each hole in the bin lid, making sure the pot sits down in the liquid. Plug in the air pump to complete the setup of your hydroponic pepper-growing system.